TROLL model currently compute leaf lifespan with Reich’s allometry (Reich et al. 1991). But we have shown that Reich’s allometry is underestimating leaf lifespan for low LMA species. Moreover simulations estimated unrealistically low aboveground biomass for low LMA species. We assumed Reich’s allometry underestimation of leaf lifespan for low LMA species being the source of unrealistically low aboveground biomass inside TROLL simulations. We decided to find a better allometry with Wright et al. (2004) GLOPNET dataset.
We tested different models starting from complet model Mcomp: \[ {LL_s}_j \sim \mathcal{logN}({\beta_0}*e^{{\beta_1}_s*{LMA_s}_j^{{\beta_3}_s} - {\beta_2}_s*{Nmass_s}_j^{{\beta_4}_s}},\,\sigma)\,\]
\[s=1,...,S_{=4}~, ~~j=1,...,n_s\] \[{\beta_i}_s \sim \mathcal{N}({\beta_i},\,\sigma_i)\,^I, ~~(\beta_i, \sigma, \sigma_i) \sim \mathcal{\Gamma}(0.001,\,0.001)\,^{2I+1}\] We tested models M1 to M9 detailed in following tabs to find the better trade-off between:
RMSEP was computed by fitting a model without a dataset and evaluating it with the same dataset. RMSEP in results are mean RMSEP for each dataset. Results are shown for each models in eahc model tabs and summarized in Results tab.
\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA - {\beta_2}_s*N,\sigma)\,\] Maximum likekihood of 9.2464903 and RMSEP of 14.773
\[ LL \sim \mathcal{logN}(\beta_0 + LMA^{{\beta_3}_s} - N^{{\beta_4}_s},\sigma)\,\] Maximum likekihood of -3.4231955 and RMSEP of 11.409
\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA^{{\beta_3}_s} - {\beta_2}_s*N^{{\beta_4}_s},\sigma)\,\] Maximum likekihood of 15.0709819 and RMSEP of 22.544
\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA - N,\sigma)\,\] Maximum likekihood of 1.3426982 and RMSEP of 12.484
\[ LL \sim \mathcal{logN}(\beta_0 + LMA^{{\beta_3}_s} - N^{{\beta_4}_s},\sigma)\,\] Maximum likekihood of -3.0373585 and RMSEP of 11.422
\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA^{{\beta_3}_s} - N^{{\beta_4}_s},\sigma)\,\] Maximum likekihood of 7.7025968 and RMSEP of 21.384
\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA,\sigma)\,\] Maximum likekihood of 4.4031261 and RMSEP of 30.281
\[ LL \sim \mathcal{logN}(\beta_0 + LMA^{{\beta_3}_s},\sigma)\,\] Maximum likekihood of -7.3836975 and RMSEP of 12.022
\[ LL \sim \mathcal{logN}(\beta_0 + {\beta_1}_s*LMA^{{\beta_3}_s},\sigma)\,\] Maximum likekihood of 9.1460414 and RMSEP of 19.767
Model M1 seemed to have shown the best trade-off between complexity (\(K=6\) parameters), convergence (see tab M1), likelihood, and prediction quality (see table 1). Figure 2 presents model prediction confidence interval and figure 3 compare Reich’s allometry and model M1 predictions with species functional traits used in TROLL. Nevertheless we will test other predictors gathered from TRY database following a model with the same response curve.
Table 1: Models likelihood and prediction quality.Root mean square errof of prediction (RMSEP) was computed by fitting a model without a dataset and evaluating it with the same dataset. RMSEP in results are mean RMSEP for each dataset.
| ML | RMSEP | |
|---|---|---|
| M1 | 9.246 | 14.77254 |
| M2 | -3.423 | 11.40898 |
| M3 | 15.071 | 22.54438 |
| M4 | 1.343 | 12.48358 |
| M5 | -3.037 | 11.42192 |
| M6 | 7.703 | 21.38398 |
| M7 | 4.403 | 30.28062 |
| M8 | -7.384 | 12.02189 |
| M9 | 9.146 | 19.76707 |
\[LL = 12.755*e^{0.007 *LMA -0.565*Nmass }\]
Maréchaux, I. & Chave, J. Joint simulation of carbon and tree diversity in an Amazonian forest with an individual-based forest model. Inprep, 1–13.
Reich, P.B., Uhl, C., Walters, M.B. & Ellsworth, D.S. (1991). Leaf lifespan as a determinant of leaf structure and function among 23 amazonian tree species. Oecologia, 86, 16–24.
Wright, I.J., Reich, P.B., Westoby, M., Ackerly, D.D., Baruch, Z., Bongers, F., Cavender-Bares, J., Chapin, T., Cornelissen, J.H.C., Diemer, M. & Others. (2004). The worldwide leaf economics spectrum. Nature, 428, 821–827.